Numerical investigation of a high head Francis turbine under steady operating conditions using foam-extend

In this work the incompressible turbulent flow in a high head Francis turbine under steady operating conditions is investigated using the open source CFD software package FOAM-extend- 3.1. By varying computational domains (cyclic model, full model), coupling methods between stationary and rotating frames (mixing-plane, frozen-rotor) and turbulence models (kω-SST, κε), numerical flow simulations are performed at the best efficiency point as well as at operating points in part load and high load. The discretization is adjusted according the y⁺-criterion with y⁺_mean > 30. A grid independence study quantifies the discretization error and the corresponding computational costs for the appropriate simulations, reaching a GCI < 1% for the chosen grid. Specific quantities such as efficiency, head, runner shaft torque as well as static pressure and velocity components are computed and compared with experimental data and commercial code. Focusing on the computed results of integral quantities and static pressures, the highest level of accuracy is obtained using FOAM in combination with the full model discretization, the mixing-plane coupling method and the κω-SST turbulence model. The corresponding relative deviations regarding the efficiency reach values of Δη_rel ~ 7% at part load, Δη_rel ~ 0.5% at best efficiency point and Δη_rel ~ 5.6% at high load. The computed static pressures deviate from the measurements by a maximum of Δp_rel = 9.3% at part load, Δp_rel = 4.3% at best efficiency point and Δp_rel = 6.7% at high load. Commercial code in turn yields slightly better predictions for the velocity components in the draft tube cone, reaching a good accordance with the measurements at part load. Although FOAM also shows an adequate correspondence to the experimental data at part load, local effects near the runner hub are captured less accurate at best efficiency point and high load. Nevertheless, FOAM is a reasonable alternative to commercial code that makes it possible to predict integral quantities and local parameters under steady operating conditions adequately.